If we have a question where we have to find the coefficient's units such as K in this case. The actual formula contains more parts but it is simply the derivatives that I am unsure about. $$K=\frac{dv}{dt}$$
Where $v=ms^{-1}$ (metres per second) and t is time
Do I simply find the derivative of $ms^{-1}$ in respect to s? And whatever units of measurement I am left with are the units of K? ie.
$$\frac{d(ms^{-1})}{ds}$$
$$=m*\frac{d(s^{-1})}{ds}$$
$$=-ms^{-2}$$
No, you just divide by the unit of time. The derivative is defined as a limit of a difference quotient: (velocity difference)/(time difference). This quotient has units (m/s)/s, and taking the limit doesn't change the unit.